Class 10 Constructions Mock Test (ICSE)

Topics in Constructions

• Construction of tangents to a circle
• Circumscribed circle of a triangle
• Inscribed circle of a triangle
• Circumscribing and inscribing regular hexagons

Constructions practice questions with answers

1. Q1Multiple choice·1 mark
   From a point $P$ outside a circle of radius $5\text{ cm}$, the length of the tangent to the circle is $12\text{ cm}$. What is the distance of point $P$ from the centre of the circle?

   1. (a)$13\text{ cm}$
   2. (b)$\sqrt{119}\text{ cm}$
   3. (c)$7\text{ cm}$
   4. (d)$17\text{ cm}$
   Show answer and step marks

   1. Correct option: (a) $13\text{ cm}$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   For the inscribed circle (incircle) of a triangle, the incentre is equidistant from all the:

   1. (a)Opposing vertices and midpoints
   2. (b)Midpoints of the sides of the triangle
   3. (c)Vertices of the triangle
   4. (d)Sides of the triangle
   Show answer and step marks

   1. Correct option: (d) Sides of the triangle+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   The circumcentre of a triangle is always the point of concurrence of the:

   1. (a)Medians of the triangle
   2. (b)Altitudes of the triangle
   3. (c)Perpendicular bisectors of the sides of the triangle
   4. (d)Angle bisectors of the triangle
   Show answer and step marks

   1. Correct option: (c) Perpendicular bisectors of the sides of the triangle+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   A circle of radius $r$ is circumscribed by a regular hexagon. What is the length of each side of this hexagon?

   1. (a)$r\sqrt{3}$
   2. (b)$\frac{r}{\sqrt{3}}$
   3. (c)$2r$
   4. (d)$\frac{2r}{\sqrt{3}}$
   Show answer and step marks

   1. Correct option: (d) $\frac{2r}{\sqrt{3}}$+1

   Answer: (d)

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